This volume contains the proceedings of a minisymposium and two AMS special sessions in three conferences: Minisymposium on All Things Hypergeometric, $q$-series and Generalizations at the 16th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA-16), June 13-17, 2022, Centre de Recherches Mathematiques, Montreal, Quebec, Canada; AMS Special Session on Hypergeometric Functions and $q$-series at the 2022 AMS Fall Western Sectional Meeting, October 22-23, 2022, University of Utah, Salt Lake City, Utah; and the AMS Special Session on Hypergeometric Functions, $q$-series and Generalizations, at the 2023 AMS Spring Eastern Virtual Sectional Meeting, April 1-2, 2023. This book provides a sampling of current mathematical research related to the Gauss hypergeometric function, and as well, its immediate generalizations and extensions. This includes the generalized hypergeometric functions that originated with Kummer, as well as such classical special functions as Lame and Heun functions. It also includes certain functions relevant to algebraic geometry, such as hypergeometric functions over finite fields. All research articles come with extensive bibliographies and can serve as entry points to the current literature.
Hypergeometric functions
Asena Cetinkaya and Dmitrii Karp, On digamma series convertible into
hypergeometric series
Howard S. Cohl, Roberto S. Costas-Santos, Loyal Durand, Camilo Montoya and
Gestur Olafsson, Double summation addition theorems for Jacobi functions of
the first and second kind
Javier Segura, On bounds for ratios of contiguous hypergeometric functions
Hans Volkmer, Expansion of the Ferrers function of the first kind in a
trigonometric series
N. S. Witte, An infinite product of incomplete Beta function-type
hypergeometric functions, and its probabilistic origins
Generalizations and Extensions
Heng Huat Chan and Teoh Guan Chua, The quadratic reciprocity law and the
Gauss-Schering lemma
Shaun Cooper, Apery-like sequences defined by four-term recurrence relations
Yifeng Huang, Ken Ono and Hasan Saad, Counting matrix points on certain
varieties over finite fields
Eleanor McSpirit and Ken Ono, Hypergeometry and the AGM over finite fields
Hans Volkmer, The Heun eigenvalue problem and some of its special cases
Yajun Zhou, Hyper-Mahler measures via Goncharov-Deligne cyclotomy
Howard S. Cohl, National Institute of Standards and Technology, Gaithersburg, MD, Roberto S. Costas-Santos, Universidad Loyola Andalucia, Sevilla, Spain, and Robert S. Maier, University of Arizona, Tucson, AZ
